تحلیل سه بعدی خمش صفحات ضخیم قطاع دایره ای مدرج تابعی چندجهته

نوع مقاله : مقاله پژوهشی

نویسنده

عضو هیات علمی / دانشکده مهندسی هوافضا، دانشگاه هوایی شهید ستاری، تهران

چکیده

در این تحقیق به تحلیل سه بعدی خمش صفحات قطاع دایره‌ای ساخته شده از مواد مدرج تابعی چند جهته پرداخته شده است. خواص ماده می‌توانند در هر سه جهت مختصاتی بر اساس تابع توانی معرفی شده تغییر کنند. معادلات حرکت و شرایط مرزی با استفاده از تئوری الاستیسیته سه‌بعدی بدست آمده است. سپس با استفاده از روش تعمیم‌یافته مربعات دیفرانسیلی، گسسته‌سازی و حل شده‌اند. نتایج عددی برای توان‌های گوناگون ماده مدرج تابعی چند جهته مورد مطالعه قرار گرفته است. نتایج نشان می‌دهد که تأثیر جهت تغییر ماده در ورق بر روی مقدار تغییر شکل صفحات ضخیم قطاع دایره‌ای، قابل توجه بوده و بنابراین می‌تواند به عنوان یکی از متغیرهای طراحی در بهینه‌سازی مورد استفاده قرار گیرد. با توجه به اینکه مسأله مورد بررسی جدید بوده و برای حل آن از تئوری الاستیسیته سه-بعدی استفاده شده است. نتایج بدست آمده در این تحقیق با نتایج حاصل از شبیه‌سازی با نرم افزار آباکوس راستی‌آزمایی شده است و تطابق خوبی را نشان می‌دهد.

کلیدواژه‌ها


عنوان مقاله [English]

Three dimensional bending analysis of multi-directional functionally graded annular sector thick plates

نویسنده [English]

  • Mostafa Livani
Department of Aerospace Engineering, Air University of Shahid Sattari, Tehran, Iran
چکیده [English]

In this paper, the three dimensional bending analysis of a multi-directional functionally graded annular sector plate is considered. The material properties are assumed to be graded in all three spatial directions following introduced power law functions. Governing Equations and boundary equations are derived based on three-dimensional theory of elasticity. The differential quadrature method is employed to discretize and solve the governing equations. Numerical results for different gradient indices are calculated. The results obtained from this research show that the direction of material variation has a noticeable effect on bending of an annular sector plate. In fact it indicates that the direction of material variation in a multi-directional annular sector plate can use as an effective variable for design optimization. Also the results of this paper can be used as benchmark for following studies. Moreover three dimensional bending analysis for an annular sector plate even for a common functionally graded plate (one directional FGM) has novelty and doesn’t considerate in literature. Comparisons are made with the solutions resulted by simulation in ABAQUS and show good agreement. Comparisons are made with the solutions resulted by simulation in ABAQUS and a good agreement was observed between the results.

کلیدواژه‌ها [English]

  • Multi-directional functionally graded materials
  • three dimensional elasticity
  • Differential Quadrature Method
  • Bending
  • annular sector plate
[1] M. Nemat-Alla, Reduction of thermal stresses by developing two-dimensional functionally graded materials, International Journal of Solids and Structures, Vol. 40, pp. 7339–7356, 2003.
[2] V. Birman, R. Chona, L. W. Byrd, M. A. Haney, Response of spatially tailored structures to thermal loading, Journal of Engineering Mathematics, Vol. 61, pp. 201–217, 2008.
[3]https://www.slideshare.net/sabihakhathun/overview-of-functionally-graded-materials-97027240
[4] https://slideplayer.com/slide/5243196/
[5] https://www.slideshare.net/byjuvtvm/analysis-of-buckling-behaviour-of-functionally-graded-plates-24296179.
[6] Functionally Graded, Geometrically Ordered Titanium Composite Armor Materials, https://investorshub.advfn.com/boards/read_msg.aspx?message_id=119919326, 2016.
[7] H. Zafarmand, M. Kadkhodayan, Three dimensional dynamic analysis and stress wave propagation in thick functionally graded plates under impact loading, Modares Mechanical Engineering, Vol. 14, No. 11, pp. 89-96, 2014. (in Persian)
[8] K. Swaminathan, D. T. Naveenkumar, A. M. Zenkour, E. Carrera, Review stress, vibration and buckling analyses of FGM plates—A state-of-the-art review, Composite Structures, Vol. 120, pp. 10-31, 2015.
[9] K. Asemi, M. Salehi, M. Akhlaghi, Three dimensional static analysis of two dimensional functionally graded plates, International Journal of Recent Advances in Mechanical Engineering, Vol. 2, No. 2, pp. 21-32, 2013.
[10] M. Alizadeh, A. Alibeigloo, Static and free vibration analyses of functionally graded sandwich plates using three dimensional theory of elasticity, Modares Mechanical Engineering, Vol. 14, No. 10, pp. 195-204, 2014. (in Persian)
[11] H. Zafarmand, M. Kadkhodayan, Three-dimensional static analysis of thick functionally graded plates using graded finite element method, Proceedings of the Institution of Mechanical Engineers Part C, Vol. 228, No. 8, pp. 1275-1285, 2014.
[12] P. Malekzadeh, Three-dimensional free vibrations analysis of thick functionally graded plates on elastic foundations, Composite Structures, Vol. 89, pp. 367-373, 2008.
[13] A. M. Zenkour, The refined sinusoidal theory for FGM plates on elastic foundations, International Journal of Mechanical Sciences, Vol. 51, pp. 869-880, 2009.
[14] M. H. Amini, M. Soleimani, A. Rastgoo, Three-dimensional free vibration analysis of functionally graded material plates resting on an elastic foundation, Smart Materials and Structures, Vol. 18, 2009.
[15] S. Benyoucef, I. Mechab, A. Tounsi, A. Fekrar, H. A. Atmane,  E. A. A. Bedia, Bending of thick functionally graded plates resting on winkler-pasternak elastic foundations, Mechanics of composite materials, Vol. 46, No. 4, 2010.
[16] A. M. Zenkour, Hygro-thermo-mechanical effects on FGM plates resting on elastic foundations, Composite Structures, Vol. 93, pp. 234-238, 2010.
[17] H. T. Thai, D. H. Choi, A refined plate theory for functionally graded plates resting on elastic foundation, Composites Science and Technology, Vol. 71, pp. 1850-1858, 2011.
[18] A. M. Zenkour, M. Sobhy, Dynamic bending response of thermoelastic functionally graded plates resting on elastic foundations, Aerospace Science and Technology, Vol. 29, pp. 7-17, 2013.
[19] V. Tahouneh, M. H. Naei, A novel 2-D six-parameter power-law distribution for three-dimensional dynamic analysis of thick multi-directional functionally graded rectangular plates resting on a two-parameter elastic foundation, Meccanica, Vol. 49, pp. 91-109, 2014.
[20] H. T. Duy, H. C. Noh, Analytical solution for the dynamic response of functionally graded rectangular plates resting on elastic foundation using a refined plate theory, Applied Mathematical Modelling, Vol. 39, pp. 6243-6257, 2015.
[21] M. Asgari, M. Akhlaghi,  S. M. Hosseini, Dynamic analysis of two-dimensional functionally graded thick hollow cylinder with finite length under impact loading, Acta Mechanica, Vol. 208, pp. 163-180, 2009.
[22] B. Sobhani Aragh, H. Hedayati, Static response and free vibration of two-dimensional functionally graded metal/ceramic open cylindrical shells under various boundary conditions, Acta Mechanica, Vol. 223, pp. 309-330, 2012.
[23] M. Shariyat, M. M., Alipour, Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations, Archive of Applied Mechanics, Vol. 81, pp. 1289-1306, 2011.
[24]  K. Asemi, M. Salehi, M. Akhlaghi, Elastic solution of a two-dimensional functionally graded thick truncated cone with finite length under hydrostatic combined loads, Acta Mechanica, Vol. 217, pp. 119-134, 2011.
[25] M. Adineh, M. Kadkhodayan, Three-dimensional thermo-elastic analysis of multi-directional functionally graded rectangular plates on elastic foundation, Acta Mechanica, pp. 1-19, 2016.
[26] A. Ghaheri, A. Nosier, Nonlinear forced vibrations of thin circular functionally graded plates, Journal of Science and Technology of Composite, Vol. 1, No. 2, pp. 1-10, 2015. (in Persian)
[27] Sh. Yousefzadeh, A. Jafari, A. Mohammadzadeh, Hydroelastic vibration analysis of functionally graded circular plate in contact with bounded fluid by Ritz method, Journal of Science and Technology of Composites, Vol. 5, No. 4, pp. 529-538, 2019. (in Persian)
[28] B. Shahriari, A. Karimian, M. R. Nazari, Onset yield analysis of rotating variable thickness disk made of functionally graded materials in engine of aero gas turbine, Modarres Mechanical Engineering, Vol. 19, No. 9, pp. 2247-2254, 2019. (in Persian)
[29] Sh. Yousefzadeh, Thermal buckling analysis of a 2-directional FGM circular plate using first-order shear deformation theory, Journal of Mechanical Engineering, Vol. 47, No. 3, pp. 307-316, 2017.  (in Persian)
[30] H.T. Thai, D.H. Choi, A refined plate theory for functionally graded plates resting on elastic foundation, Composites Science and Technology, Vol. 71, pp. 1850–1858, 2011.